Let's analyze each statement to find the correct ones.

1. First Statement:

   • "Если каждый элемент множества $C$ принадлежит и множеству $A$, и множеству $B$, то множество $C$ называется пересечением множеств $A$ и $B$."
   • This is the correct definition of the intersection of two sets. The intersection $A \cap B$ consists of elements that belong to both $A$ and $B$.

2. Second Statement:

   • $(A \cap B) \Leftrightarrow (B \cap A)$
   • This is true because the intersection operation is commutative, meaning $A \cap B = B \cap A$.

3. Third Statement:

   • $\overline{A \setminus B} = \overline{A} \cap B$
   • This is false. The correct relation involving set difference and complements is $\overline{A \setminus B} = \overline{A} \cup B$, not $\cap$.

4. Fourth Statement:

   • "Утверждение 'любое чётное число, начиная с 4, можно представить в виде суммы двух простых чисел' является высказыванием."
   • This is true because it refers to Goldbach's conjecture, which is a well-known mathematical statement (although not proven for all even numbers).

Correct Statements:

• The first, second, and fourth statements are true.
• The third statement is false.

Do you have any questions or need further clarification?

Here are 5 relative questions for deeper exploration:

1. What are the formal properties of the set union operation?
2. How does De Morgan’s Law relate to set complements and unions/intersections?
3. What are some practical applications of set theory in computer science?
4. What is the importance of Goldbach’s conjecture in number theory?
5. How does the commutative property apply to other set operations like union and difference?

Tip: When dealing with sets, always check if operations are commutative or associative to simplify your calculations.